期刊文献+

矩阵方程X+A^(*)(R+B^(*)XB)^(-t)A=Q的Hermite正定解

Hermite positive definite solution of the matrix equation X+A^(*)(R+B^(*)XB)^(-t)A=Q
下载PDF
导出
摘要 非线性矩阵方程X+A^(*)(R+B^(*)XB)^(-t)A=Q(t≥1)来源于离散时间代数Riccati方程.本文给出该方程存在Hermite正定解的充分条件及上下界估计,构造了求解该矩阵方程的不动点迭代和免逆迭代算法,运用单调有界定理证明了算法的收敛性,最后通过数值算例说明所提算法对求解该矩阵方程的有效性及可行性. The nonlinear matrix equation X+A^(*)(R+B^(*)XB)^(-t)A=Q(t≥1)is derived from the discrete-time algebraic Riccati equation.The sufficient conditions for the existence of Hermite positive definite solutions and the upper and lower bounds are given.The fixed point iteration and inverse-free iteration algorithms for solving the equation are constructed and the convergence of the algorithm is proved by using the monotone boundedness theorem.Finally,two numerical examples are given to illustrate the effectiveness and feasibility of the proposed algorithm for solving the matrix equation.
作者 黄玉莲 罗显康 HUANG Yulian;LUO Xiankang(Faculty of Science,Yibin University,Yibin,Sichuan 644000,China;Yibin Nanxi Vocational and Technical School,Yibin,Sichuan 644100,China)
出处 《内江师范学院学报》 CAS 2023年第12期61-67,85,共8页 Journal of Neijiang Normal University
基金 宜宾学院高层次人才“启航”计划项目(2019QD07)。
关键词 非线性矩阵方程 RICCATI方程 HERMITE正定解 上下界 迭代算法 nonlinear matrix equation Riccati equation Hermite positive definite solution upper and lower bounds iterative method
  • 相关文献

参考文献6

二级参考文献47

  • 1蒋永泉.矩阵方程aX^2+bX+cE=O的正定解和实对称解[J].大学数学,2005,21(2):113-115. 被引量:4
  • 2陈小山,黎稳.关于矩阵方程X+A~*X^(-1)A=P的解及其扰动分析[J].计算数学,2005,27(3):303-310. 被引量:19
  • 3Xiao xia Guo.ON HERMITIAN POSITIVE DEFINITE SOLUTION OF NONLINEAR MATRIX EQUATION X+A^*X^-2A=Q[J].Journal of Computational Mathematics,2005,23(5):513-526. 被引量:9
  • 4Bhatia R. Matrix Analysis, Springer, Berlin, 1997.
  • 5Salah M. E1-Sayed and Asmaa M. A1-Dbiban. On positive definite solutions of the nonlinear matrix equation X + A^*X^-nA = I[M]. Appl. Math. Comput., 2004, 151: 533-541.
  • 6Salah M. E1-Sayed and Milko G. Petkov. Iterative methods for nonlinear matrix equation X + A^*X-αA = I(α > 0)[J]. Linear Algebra Appl., 2005, 403: 45-52.
  • 7Jacob C. Engwerda, Andre C. M. Ran and Arie L. Rijkeboer. Necessary and sumcient conditions for the existence of a positive definite solution of the matrix equation X + A^*X^-1A = Q[J]. Linear Algebra Appl., 1993, 186: 255-275.
  • 8Jacob C. Engwerda. On the existence of a positive definite solution of the matrix equation X + A^TX^-1A = I[J]. Linear Algebra Appt., 1993, 194: 91-108.
  • 9Furuta T. Operator inequalities associated with Holder-McCarthy and Kantorovich inequalities[J]. J. Inequal. Appl., 1998, 6: 137-148.
  • 10Chunhua Guo and Peter Lancaster, Iterative solution of two matrix equations[J]. Math. Comput., 1999, 68: 1589-1603.

共引文献9

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部